Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions.

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA).

Wannier interpolation of one-particle Green's functions from coupled-cluster singles and doubles (CCSD).

We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within a coupled-cluster singles and doubles (CCSD) method for a periodic system. These schemes use Wannier orbitals for circumventing huge cost for a large number of sampled k points. One of the schemes is the direct interpolation, which obtains the GF straightforwardly by using Fourier transformation.

One-particle Green's function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn-Sham system.

For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schrödinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous eigenstates of the energy and total spin for the first time. The solutions for the three-electron system allow us to derive analytic expressions for the exact one-particle Green's function (GF) for the corresponding two-electron system. We calculate the GF in frequency domain to examine systematically its behavior depending on the electronic interactions.

Quasiparticle energy spectra of isolated atoms from coupled-cluster singles and doubles (CCSD): Comparison with exact CI calculations.

In this study, we have calculated single-electron energy spectra via the Green's function based on the coupled-cluster singles and doubles (GFCCSD) method for isolated atoms from H to Ne. In order to check the accuracy of the GFCCSD method, we compared the results with the exact ones calculated from the full-configuration interaction. Consequently, we have found that the GFCCSD method reproduces not only the correct quasiparticle peaks but also satellite ones by comparing the exact spectra with the 6-31G basis set.

Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD).

We demonstrate in the present study that self-consistent calculations based on the self-energy functional theory (SFT) are possible for the electronic structure of realistic systems in the context of quantum chemistry. We describe the procedure of a self-consistent SFT calculation in detail and perform the calculations for isolated 3d transition metal atoms from V to Cu as a preliminary study. We compare the one-particle Green's functions obtained in this way and those obtained from the coupled-cluster singles and doubles method.

Band structures in coupled-cluster singles-and-doubles Green's function (GFCCSD).

We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect.

Quantum Singwi-Tosi-Land-Sjölander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results.

For inhomogeneous interacting electronic systems under a time-dependent electromagnetic perturbation, we derive the linear equation for response functions in a quantum mechanical manner. It is a natural extension of the original semi-classical Singwi-Tosi-Land-Sjölander (STLS) approach for an electron gas. The factorization ansatz for the two-particle distribution is an indispensable ingredient in the STLS approaches for the determination of the response function and the pair correlation function.

A Novel Intrinsic Interface State Controlled by Atomic Stacking Sequence at Interfaces of SiC/SiO.

On the basis of ab initio total-energy electronic-structure calculations, we find that electron states localized at the SiC/SiO interface emerge in the energy region between 0.3 eV below and 1.2 eV above the bulk conduction-band minimum (CBM) of SiC, being sensitive to the sequence of atomic bilayers in SiC near the interface.

Interstitial channels that control band gaps and effective masses in tetrahedrally bonded semiconductors.

We find that electron states at the bottom of the conduction bands of covalent semiconductors are distributed mainly in the interstitial channels and that this floating nature leads to the band-gap variation and the anisotropic effective masses in various polytypes of SiC. We find that the channel length, rather than the hexagonality prevailed in the past, is the decisive factor for the band-gap variation in the polytypes. We also find that the floating nature causes two-dimensional electron and hole systems at the interface of different SiC polytypes and even one-dimensional channels near the inclined SiC surface.

Floating electron states in covalent semiconductors.

We report first-principles electronic-structure calculations that clarify the floating nature of electron states in covalent semiconductors. It is found that wave functions of several conduction- and valence-band states, including the conduction-band minima, do not distribute near atomic sites, as was taken for granted, but float in interstitial channels in most semiconductors. The directions and shapes of the interstitial channels depend on the crystal symmetry so that mysterious variation of the energy gaps in SiC polymorphs is naturally explained by considering the floating nature.